Physics Commons^™

Distortion And Evolution Of A Localized Vortex In An Irrotational Flow, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

This paper examines the interaction of an axisymmetric vortex monopole, such as a Lamb vortex, with a background irrotational flow. At leading order, the monopole is advected with the background flow velocity at the center of vorticity. However, inhomogeneities of the flow will cause the monopole to distort. It is shown that a shear‐diffusion mechanism, familiar from the study of mixing of passive scalars, plays an important role in the evolution of the vorticity distribution. Through this mechanism, nonaxisymmetric vorticity perturbations which do not shift the center of vorticity are homogenized along streamlines on a Re1/3 time scale, much faster …

Wing-Section Optimization For Supersonic Viscous Flow, Cem Cihan Item

Mechanical & Aerospace Engineering Theses & Dissertations

The recent interest in the High Speed Civil Transport (HSCT) has resulted in renewed research studies of optimized supersonic cruise transport configurations. Incorporation of flow viscosity effects in the design process of such a supersonic wing is currently under investigation. This may lead to more accurate problem formulations and, in tum, greater aerodynamic efficiency than can be obtained by the traditional, inviscid, linear theories. In this context, for a design code to be a candidate for a complex optimization problem, such as three-dimensional viscous supersonic wing design, it should be validated using simpler building-block shapes.

To optimize the shape of …

A Direct Numerical Simulation Of Vortex Breakdown Induced Tail Buffet, Steven James Massey

Mechanical & Aerospace Engineering Theses & Dissertations

A simulation of tail buffet is presented for a delta wing-vertical tail configuration. Flow conditions are chosen such that the wing primary-vortex cores experience vortex breakdown and the resulting turbulent wake flow impinges on the vertical tail. The dimensions and material properties of the vertical tail are chosen such that the deflections are large enough to insure interaction with the flow, and the natural frequencies are high enough to facilitate a practical computational solution. This multidisciplinary problem is solved sequentially for the fiuid flow, the elastic deformations and the grid displacements. The fluid flow is simulated by time accurately solving …

Optical Properties Of Human Uterus At 630 Nm, Steen J. Madsen, Bruce J. Tromberg, Yona Tadir, Pius Wyss, Lars O. Svaasand, Richard C. Haskell

All HMC Faculty Publications and Research

The optical properties of normal and fibriotic human uteri were determined using frequency-domain and steady-state techniques .

Frequency-Domain Photon Migration In Turbid Media, Bruce J. Tromberg, Steen J. Madsen, Curtis Chapman, Lars O. Svaasand, Richard C. Haskell

All HMC Faculty Publications and Research

An analytical model is presented for the propagation of diffuse photon density waves in turbid media. The frequency- and wavelength-dependence of photon density waves are measured using Frequency-domain Photon Migration (FDPM). Media optical properties, including absorption, transport, and fluorescence relaxation times are calculated from experimental results.

A Fast Numerical Solution Of Scattering By A Cylinder: Spectral Method For The Boundary Integral Equations, Fang Q. Hu

Mathematics & Statistics Faculty Publications

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converge slowly for high frequency waves. In this paper, a fast numerical solution is presented for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of …

Electrostatic Positioning Of Droplets In Turbulent Flows (Lstm 375/Te/93), Nihad E. Daidzic, Adrian Melling

Aviation Department Publications

Report LSTM 375/TE/93, Lehrstuhl fuer Stroemungsmechanik Universitaet Erlangen-Nuernberg Cauerstr. 4, 8520 Erlangen Germany.

A Numerical Study Of Wave Propagation In A Confined Mixing Layer By Eigenfunction Expansions, Fang Q. Hu

Mathematics & Statistics Faculty Publications

It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance …

Induced Mach Wave-Flame Interactions In Laminar Supersonic Fuel Jets, F. Q. Hu, T. L. Jackson, D. G. Lasseigne, C. E. Grosch

Mathematics & Statistics Faculty Publications

A model problem is proposed to investigate the steady response of a reacting, compressible laminar jet to Mach waves generated by wavy walls in a channel of finite width. The model consists of a two-dimensional jet of fuel emerging into a stream of oxidizer which are allowed to mix and react in the presence of the Mach waves. The governing equations are taken to be the steady parabolized Navier-Stokes equations which are solved numerically. The kinetics is assumed to be a one-step, irreversible reaction of the Arrhenius type. Two important questions on the Mach wave-flame interactions are discussed: (i) how …

Erratum: "Temperature And Suction Effects On The Instability Of An Infinite Swept Attachment Line" [Physics Of Fluids A 4, 2008 (1992)], D. G. Lasseigne, T. L. Jackson, F. Q. Hu

Mathematics & Statistics Faculty Publications

Erratum to:

Lasseigne, D. G., Jackson, T. L., & Hu, F. Q. (1992). Temperature and suction effects on the instability of an infinite swept attachment line. Physics of Fluids A: Fluid Dynamics, 4(9), 2008-2012. doi:10.1063/1.858370

Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic

Aviation Department Publications

In this study the instability of droplets and cylindrical jets is investigated. The understanding of these processes has both academic and practical value. Instability of cylindrical jets is theoretically investigated for infinitesimal and finite, but small initial amplitudes (linear and nonlinear stability). For droplets, only linear theory is presented. It is assumed that the capillary force play a dominant role. It is determined that the viscosity exerts a damping effect. In the first section we give an introduction, after which the linear stability theory of cylindrical liquid jets is presented. In the third section the nonlinear jet stability theory is …

Temperature And Suction Effects On The Instability Of An Infinite Swept Attachment Line, D. G. Lasseigne, T. L. Jackson, F. Q. Hu

Mathematics & Statistics Faculty Publications

It is known that the incompressible, infinite swept attachment line flow is unstable to streamwise disturbances that originate in the boundary layer when the cross-flow exceeds a critical magnitude. Furthermore, a small degree of suction at the surface has a significant stabilizing influence while a small degree of blowing has a considerable destabilizing influence. This paper investigates the stabilizing and destabilizing effects of, respectively, cooling or heating the plate and the competing or enhancing effects of suction or blowing. A nonorthogonal flow with respect to the attachment line is also considered by adding a component of shear to the mean …

Parametric Instability Of Supersonic Shear Layers Induced By Periodic Mach Waves, Fang Q. Hu, Christopher K. W. Tam

Mathematics & Statistics Faculty Publications

It is suggested that parametric instability can be induced in a confined supersonic shear layer by the use of a periodic Mach wave system generated by a wavy wall. The existence of such an instability solution is demonstrated computationally by solving the Floquet system of equations. The solution is constructed by means of a Fourier-Chebyshev expansion. Numerical convergence is assured by using a very large number of Fourier and Chebyshev basis functions. The computed growth rate of the induced flow instability is found to vary linearly with the amplitude of the mach waves when the amplitude is not excessively large. …

Nonlinear-Interaction Of A Detonation Vorticity Wave, D. G. Lasseigne, T. L. Jackson, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multidomain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results whenever obtained in this study agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient …

An Evolution Operator Solution For A Nonlinear Beam Equation, Carl E. Crockett

Theses and Dissertations

A nonlinear partial differential equation, motivated by the transverse vibration of a beam, is shown to have a unique solution. The existence theory, which is in the setting of semigroups and evolution operators, is a composite and synthesis of theorems of Kato. The formulation of the problem and the verification that the formulation leads to a solution are new. The introductory chapter provides background on the topic generally. Chapter 2 provides detailed formulations for the constant coefficient case. Chapter 3 describes nonautonomous cases. The general theorem is presented here. In Chapter 4, a more general case is considered. Namely, Kelvin …

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

On A Moving Boundary Problem Of Transitional Ballistics, Jen-Ing G. Hwang

Mathematics & Statistics Theses & Dissertations

A major problem which arises in computer simulation of the firing of a gun weapon is the development of numerical schemes which effectively account for the physics of projectile motion. The chief difficulty is that away from the projectile the calculation is ordinarily accomplished on a fixed numerical grid, whereas due to projectile movement some cells of the grid near the projectile undergo volume changes as the calculation proceeds. A local finite volume scheme is developed which accounts for the expansion or compression of cells fore-and-aft of the projectile. Through the process of numerical experiment, the effectiveness of the scheme …

On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from …